time step selection

Hello, I have a CFD project (using Fluent Software) which deals with blood flow within an aortic model. I use the implicit formulation and a periodic inlet velocity profile with period of 0.86 sec. I will greatly appreciate advices regarding the best technique to select the appropriate time step for the unsteady solution, at least how to select the magnitude of order..

The time step for unsteady flow is generally taken as a constant value with a tradeoff between temporal accuracy and speed of computation and the stability, which is unfortunately non-linear. A step of 1e-2 to 1e-3 is the most preferred, but it defintely depends on the problem and grid at hand.

Dear Ganesh, Thank you for your help. How did you define this time step? according to your experience or the time period? In fact I tried two time steps - 5e-3 and 1e-3 (172 or 860 steps per cycle) which resulted in similar flow field. To validate it I compared the axial veloity at a specific cross section and the general flow field. Are there any additional methods that I may be missing to check stability and accuracy in Fluent?

I am not sure about Fluent, because I have my own solver. The stability is unfortunately non-linear and the time step therfore is a fuction of the grid and the problem. The outer time step(as it is generally called, as also in Fluent which uses Dual time stepping)is therfore a matter of experience, with due respet to issues of stability, speed of computation and accuracy. In fact it is always a nice idea to use two time steps as you did, for a cross check, but will not be a good one in the industrial environment, where quick answers are required, wherein the experience of runnung such cases will prove handy.

if this might help, I recently read in a matter related with fluctuating turbulent variables, the time mean of a turbulent function, when defined i.e. for u,v, p. , goes like an averaging period taken to be longer than any significant period of the fluctuations themselves, For turbulent gas nad water flows an averaging time period of 5 seconds is quite usually adequate, so your quest may answered in such observations in the real world experiments and length scale settings, regards, taw

if you want to see a magic number, try the CFL condition (Courant-Friedrichs-Lewy); usually shortened as Courant number. Unfortunately, it really matters when explicit time differencing scheme is to be imposed because it is a stability criterion. It simply says how long it'll take for a particle (flow) to pass through a computational element. With the implicit scheme there is no problem with stability therefore you can choose whatever time step you like but you should be aware of the physics you want to model. Additionally, the larger the time step, the worse accuracy; this apply to implicit schemes especially.

absolute numbers are meaningless, here. the only way to make sense of this is to put it in non-dimensional terms.

let's say we use an implicit method (which is very much recommended) so we can ignore the issue of stability. your time step will then be bounded by a required minimum and maximum.

the maximum stems from a requirement for accuracy: the time step has to be small enough to resolve the dominant unsteadiness in your type of flow. obviously this very much depends on the flow, but you can define a requirement in non-dimensional terms as: there should be in the order of 30-40 time steps within one period of the highest significant frequency in your problem. to give you one example: incompressible vortex shedding off a cylinder occurs at a strouhal number of roughly 0.2. knowing that, you will define your time step in such a way as to resolve the expected time period by roughly 30-40 steps. the catch is: you need to have a relatively good expectation for the occurring frequencies. if you have no clue you can always make some estimation based on flow velocities and length scales of your problem, and then follow ganesh's advice to try a number of different time steps in order to find a converged solution. the absolute value for the maximum for your time step could be 1e-3 or 1e+3, or anything else. it really depends on the nature and dimensions of your flow. in any case: the dominant frequency needs to be resolved.

the minimum is given by the requirement to keep your time step large enough for validity of your turbulence model (if any). if you're solving the RANS equations, you need to make sure that the time average is well defined, i.e. your time step should be significantly larger than the dominant turbulent time scales. most people give this issue less thought than the above requirement for accuracy, based on the assumption that they won't even get close to turbulent scales.

Hello. blood is a non-newtonian fluid. so its equations and time step choosing differ from navier stocks.any way for newtonian fluids 1e-6 to 1e-4 is an appropriate selection for combustion. and i think 1e-3 would be appropriate for noncombustion applications. if you want i can explain you a methode valid for combustion.